A generalized parallel task model for recurrent real-time processes

A model is considered for representing recurrent precedence-constrained tasks that are to execute on multiprocessor platforms. A recurrent task is specified as a directed acyclic graph (DAG), a period, and a relative deadline. Each vertex of the DAG represents a sequential job, while the edges of the DAG represent precedence constraints between these jobs. All the jobs of the DAG are released simultaneously and need to complete execution within the specified relative deadline of their release. Each task may release j

Scheduling periodic tasks in a hard real-time environment

We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks $au_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $au_i$ releases a job of running time $c_i$ at each time $a_i + kcdot p_i,k in mathbb{N}_0$ and a collision occurs if two jobs are simultaneously active on the same machine. We shed some light on the complexity and approximability landscape of this problem. Although the problem cannot be approximated within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i | p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads to a 2-approximation. This result is tight, even asymptotically

A General Buffer Scheme for the Windows Scheduling Problem

Broadcasting is an efficient alternative to unicast for delivering popular on-demand media requests. Broadcasting schemes that are based on windows scheduling algorithms provide a way to satisfy all requests with both low bandwidth and low latency. Consider a system of n pages that need to be scheduled (transmitted) on identical channels an infinite number of times. Time is slotted, and it takes one time slot to transmit each page. In the windows scheduling problem (WS) each page i, 1 ≤ i ≤ n, is associated with a request window wi. In a feasible schedule for WS, page i must be scheduled at least once in any window of wi time slots. The objective function is to minimize the number of channels required to schedule all the pages. The main contribution of this paper is the design of a general buffer scheme for the windows scheduling problem such that any algorithm for WS follows this scheme. As a result, this scheme can serve as a tool to analyze and/or exhaust all possible WS-algorithms. The buffer scheme is based on modelling the system as a nondeterministic finite state machine in which any directed cycle corresponds to a legal schedule and vice-versa. Since WS is NP-hard, w

A model-based approach for multiple QoS in scheduling: from models to implementation

Meeting multiple Quality of Service (QoS) requirements is an important factor in the success of complex software systems. This paper presents an automated, model-based scheduler synthesis approach for scheduling application software tasks to meet multiple QoS requirements. As a first step, it shows how designers can meet deadlock-freedom and timeliness requirements, in a manner that (i) does not over-provision resources, (ii) does not require architectural changes to the system, and that (iii) leaves enough degrees of freedom to pursue further properties. A major benefit of our synthesis methodology is that it increases traceability, by linking each scheduling constraint with a specific pair of QoS property and underlying platform execution model, so as to facilitate the validation of the scheduling constraints and the understanding of the overall system behaviour, required to meet further QoS properties. The paper shows how the methodology is applied in practice and also presents a prototype implementation infrastructure for executing an application on top of common operating systems, without requiring modifications of the latter

Solving an Avionics Real-Time Scheduling Problem by Advanced IP-Methods

We report on the solution of a real-time scheduling problem that arises in the design of software-based operation control of aircraft. A set of tasks has to be distributed on a minimum number of machines and offsets of the tasks have to be computed. The tasks emit jobs periodically starting at their offset and then need to be executed on the machines without any delay. Also, further constraints in terms of memory usage and redundancy requirements have to be met. Approaches based on standard integer programming formulations fail to solve our real-world instances. By exploiting structural insights of the problem we obtain an IP-formulation and primal heuristics that together solve the real-world instances to optimality and outperform text-book approaches by several orders of magnitude. Our methods lead, for the first time, to an industry strength tool to optimally schedule aircraft sized problems

Mixed-Criticality Scheduling of Sporadic Task Systems

We consider the scheduling of mixed-criticality task systems, that is, systems where each task to be scheduled has multiple levels of worst-case execution time estimates. We design a scheduling algorithm, EDF-VD, whose effectiveness we analyze using the processor speedup metric: we show that any 2-level task system that is schedulable on a unit-speed processor is correctly scheduled by EDF-VD using speed $\phi$; here \phi < 1.619 is the golden ratio. We also show how to generalize the algorithm to $K > 2$ criticality levels. We finally consider 2-level instances on $m$ identical machines. We prove speedup bounds for scheduling an independent collection of jobs and for the partitioned scheduling of a 2-level task system

Schedulability analysis of non-preemptive recurring real-time tasks

10.1109/IPDPS.2006.163940620th International Parallel and Distributed Processing Symposium, IPDPS 2006200

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Not AvailableThe aim of this study was to characterize the soil fertiltiy like pH, organic carbon (OC), available nitrogen (N), available potassium (P) and available phosphorus (K), and DTPA extractable iron (Fe), manganese (Mn), zinc (Zn) and copper (Cu) of lower Brahmaputra valley of Assam using multivariate statistics (principal component, correlation matrix and cluster analysis). A total of 2753 soil samples from a depth of 0-25 cm at an approximate interval of 1 km were collected from Barpeta, Bongaigaon and Nalbari districts of Assam. Soil properties showed large variability with greatest variation was observed in DTPA-Zn (120%), whereas the smallest variation was in pH (17.5%). The principal component analysis (PCA) applied on the investigated soil properties identified three components with eigen values greater than 1, which explained 65% variability and same grouping was also obtained from cluster analysis. Cluster 1 includes Zn, Cu, pH, Fe, P and Mn, which has highest loading in PC1 and also showed strong significant relationship. Cluster 2, which contains OC and N, and had highest loading in PC2 and also showed the significant positive relationship with each other. Cluster 3 contain only K, which is equally distributed both in PC1 and PC2 and also significantly and positively correlated with pH, Fe, Zn and Cu of cluster 1 and OC and N of cluster 2.Not Availabl

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